A company's stock was selling at

HELP ASAP!!!!!! Ken and Betty each write a proof of the statement: if m

shepuryov [24]

The statement third "Betty wrote an indirect proof using contradiction' and statement fourth "Ken wrote direct proof using deductive evidence" are correct.

<h3>What is an angle?</h3>

When two lines or rays converge at the same point, the measurement between them is called a "Angle."

We have Ken's statements are shown in the table:

Angle AOC = Angle BOD (given)

Angle AOB + Angle BOC = Angle BOC + Angle COD (angle addition postulate)

Angle AOB = ANgle COD (subtraction property of equality)

Ken wrote direct proof using deductive evidence.

As we can in betty's proof:

Betty wrote an indirect proof using contradiction.

Thus, the statement third "Betty wrote an indirect proof using contradiction' and statement fourth "Ken wrote direct proof using deductive evidence" are correct.

Learn more about the angle here:

brainly.com/question/7116550

#SPJ1

3 0

2 years ago

How many 4' x 8' sheets of plywood are required to cover a floor that is 9 m by 16 m?

Xelga [282]

Assuming no border or waste, 9m by 16 m translates to 29.52' x 52.49'.
use 32/8=4 sheets of plywood to cover the width on the 8' side.
For the length, use 52/4=13 pieces on the 4' side.
This gives a total of 4*13=52 sheets.
The extra 0.49' x 29.52 can be covered using the extra from the last four sheets for the width.

Check:
Area to be covered: 29.52*52.49=1550 sq. ft.
Area of plywood supplied = 52*4'x8'= 1664 sq. ft, > 1550 sq.ft.

8 0

3 years ago

ANSWER ALL 5 PARTS.

N76 [4]

A function $f$ from a set A to a set B is defined as a relation that assings to each element $x$ in the set A exactly one element $y$ in the set B. The set A is called the domain of the function while the set B is the range. So we have five statements and need to find some functions. Melissa decides to reserve a patch in her vegetable garden for growing bell peppers. If each side of the tomato patch is $x$ feet, then we have a square patch as shown in the Figure below.

1.a) Write the function Wa(x) representing the width of the bell pepper patch.

We know that she wants its width to be half the width of the tomato patch. Let $x$ be the width of the tomato patch, then the function that matches this statement is:

$\boxed{Wa(x)=\frac{x}{2}}$

1.b) Write the function La(x) representing the length of the bell pepper patch.

In this case Melissa wants its length to exceed the length of the tomato patch by 2 feet. To do this we enlarge the length of the tomato patch 2 feet. Therefore the function is the following:

 $\boxed{La(x)=x+2}$

2. Area of the bell pepper patch in terms of x.

Given that the bell pepper patch is a rectangle, then the area of a rectangle is the product of the length and width. So:

 $A=(\frac{x}{2})(x+2) \\ \\ \therefore \boxed{A=\frac{x(x+2)}{2}}$

3. Combined area of the tomato patch and the bell pepper patch.

This function is the sum of both the area of the tomato patch and the bell pepper patch. So:

 $Aar(x)=x^{2}+\frac{x(x+2)}{2} \rightarrow Aar(x)=x^{2}+ \frac{x^{2}}{2}+x \rightarrow Aar(x)=\frac{3x^{2}}{2}+x \\ \\ \therefore \boxed{Aar(x)=\frac{x(3x+2)}{2}}$

4. Write the function Aa(x) for the remaining planting area in the garden.

The remaining planting area in the garden are the rectangles in red. So we need to subtract the width of the bell pepper patch from the width of the tomato patch and multiply it by 2. In mathematical language this is given by:

 $Aa(x)=2(x-\frac{x}{2}) \rightarrow Aa(x)=x$

5. Find the area of the remaining space in the garden after planting tomatoes and bell peppers.

Given that Melissa wants the area of the bell pepper patch to be 31.5 square feet, then it is true that:

 $31.5=\frac{x(x+2)}{2} \rightarrow x^{2}+2x-64=0 \\ \\ solving \ for \ x: \\ x=7.06$

Therefore the area of the remaining space is:

 $\boxed{Aa(7.06)=7.06ft^{2}}$